{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "729d4530",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "08e91569",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 201)\n",
      "(1, 101)\n",
      "(101, 201)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Load the .mat file\n",
    "mat_data = scipy.io.loadmat('Allen_Cahn.mat')\n",
    "\n",
    "# Following is the code to plot the data u vs x and t. u is 256*100\n",
    "# matrix. Use first 75 columns for training and 25 for testing :)\n",
    "\n",
    "# Access the variables stored in the .mat file\n",
    "# The variable names in the .mat file become keys in the loaded dictionary\n",
    "x = mat_data['x']\n",
    "t = mat_data['t']\n",
    "u = mat_data['u']\n",
    "\n",
    "# Use the loaded variables as needed\n",
    "print(x.shape)\n",
    "print(t.shape)\n",
    "print(u.shape)\n",
    "\n",
    "X, T = np.meshgrid(x, t)\n",
    "# Define custom color levels\n",
    "c_levels = np.linspace(np.min(u), np.max(u), 100)\n",
    "\n",
    "# Plot the contour\n",
    "plt.figure()\n",
    "plt.figure(figsize=(15, 5))\n",
    "plt.contourf(T, X, u, levels=c_levels, cmap='coolwarm')\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x')\n",
    "plt.title('Allen-cahn-Equation')\n",
    "plt.colorbar()  # Add a colorbar for the contour levels\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ddc2111e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "\n",
    "\n",
    "# Define the GRU model\n",
    "class GRU(nn.Module):\n",
    "    def __init__(self, input_size, hidden_size, output_size):\n",
    "        super(GRU, self).__init__()\n",
    "\n",
    "        self.hidden_size = hidden_size\n",
    "\n",
    "        self.gru = nn.GRU(input_size, hidden_size, batch_first=True)\n",
    "        self.fc = nn.Linear(hidden_size, output_size)\n",
    "\n",
    "    def forward(self, x, hidden):\n",
    "        output, hidden = self.gru(x, hidden)\n",
    "        output = self.fc(output)\n",
    "        return output, hidden\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bd76b85c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "# Load the .mat file\n",
    "mat_data = scipy.io.loadmat('X.mat')\n",
    "\n",
    "X = mat_data['X']\n",
    "\n",
    "mat_data1 = scipy.io.loadmat('y_pred.mat')\n",
    "\n",
    "u1 = mat_data1['y_pred']\n",
    "\n",
    "np.set_printoptions(threshold=np.inf)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ee997f1e",
   "metadata": {},
   "outputs": [],
   "source": [
    "u1 = u1.reshape(101, 201)\n",
    "u1_new = u1.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "47f45445",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "\n",
    "X, T = np.meshgrid(x, t)\n",
    "\n",
    "# # Define custom color levels\n",
    "c_levels = np.linspace(np.min(u1_new),  np.max(u1_new), 100)\n",
    "\n",
    "# Plot the contour\n",
    "plt.figure()\n",
    "plt.figure(figsize=(15, 5))\n",
    "plt.contourf(T, X, u1_new.T, levels=c_levels, cmap='coolwarm')\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x')\n",
    "plt.title('Allen-cahn-Equation')\n",
    "plt.colorbar()  # Add a colorbar for the contour levels\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7d7be168",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Toy problem data\n",
    "input_size = 201  # number of columns in a dataset\n",
    "hidden_size = 32  # number of neurons\n",
    "output_size = 201\n",
    "sequence_length = 80  # number of sequences/ number of rows\n",
    "batch_size = 1\n",
    "num_epochs = 2000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d8ae5671",
   "metadata": {},
   "outputs": [],
   "source": [
    "# data = scipy.io.loadmat('y_pred.mat')\n",
    "u1 = u1_new\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5928f808",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test data shape (201,)\n",
      "input data shape (201, 80)\n",
      "Target data shape (201, 80)\n"
     ]
    }
   ],
   "source": [
    "input_data = u1[:, 0:80]\n",
    "target_data = u1[:, 1:81]\n",
    "\n",
    "test_data = u1[:, 80] ### Change here\n",
    "#test_target = u1[:, 81:101]\n",
    "\n",
    "print(\"test data shape\", test_data.shape)\n",
    "#print(\"test target shape\", test_target.shape)\n",
    "\n",
    "print(\"input data shape\",input_data.shape)\n",
    "print(\"Target data shape\",target_data.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c22cbe9f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "input tensor shape torch.Size([1, 80, 201])\n",
      "Target tensor shape torch.Size([1, 80, 201])\n"
     ]
    }
   ],
   "source": [
    "# Convert data to tensors\n",
    "input_tensor = torch.tensor(input_data.T).view(batch_size, sequence_length, input_size).float()\n",
    "target_tensor = torch.tensor(target_data.T).view(batch_size, sequence_length, output_size).float()\n",
    "\n",
    "print(\"input tensor shape\",input_tensor.shape)\n",
    "print(\"Target tensor shape\",target_tensor.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5eda88e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convert test data to tensors\n",
    "test_tensor = torch.tensor(test_data.T).view(batch_size, 1, input_size).float()\n",
    "#test_target_tensor = torch.tensor(test_target.T).view(batch_size, 20, output_size).float()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "54f03541",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 10/2000, Loss: 0.0001776106801117\n",
      "Epoch: 20/2000, Loss: 0.0000249337972491\n",
      "Epoch: 30/2000, Loss: 0.0000130836551762\n",
      "Epoch: 40/2000, Loss: 0.0000049786908676\n",
      "Epoch: 50/2000, Loss: 0.0000032534019283\n",
      "Epoch: 60/2000, Loss: 0.0000027924322694\n",
      "Epoch: 70/2000, Loss: 0.0000022845495096\n",
      "Epoch: 80/2000, Loss: 0.0000016522802753\n",
      "Epoch: 90/2000, Loss: 0.0000010800126802\n",
      "Epoch: 100/2000, Loss: 0.0000009060862567\n",
      "Epoch: 110/2000, Loss: 0.0000009040709870\n",
      "Epoch: 120/2000, Loss: 0.0000009032849562\n",
      "Epoch: 130/2000, Loss: 0.0000009032849562\n",
      "Epoch: 140/2000, Loss: 0.0000009032849562\n",
      "Epoch: 150/2000, Loss: 0.0000009032849562\n",
      "Epoch: 160/2000, Loss: 0.0000009032849562\n",
      "Epoch: 170/2000, Loss: 0.0000009032849562\n",
      "Epoch: 180/2000, Loss: 0.0000009032849562\n",
      "Epoch: 190/2000, Loss: 0.0000009032849562\n",
      "Epoch: 200/2000, Loss: 0.0000009032849562\n",
      "Epoch: 210/2000, Loss: 0.0000009032849562\n",
      "Epoch: 220/2000, Loss: 0.0000009032849562\n",
      "Epoch: 230/2000, Loss: 0.0000009032849562\n",
      "Epoch: 240/2000, Loss: 0.0000009032849562\n",
      "Epoch: 250/2000, Loss: 0.0000009032849562\n",
      "Epoch: 260/2000, Loss: 0.0000009032849562\n",
      "Epoch: 270/2000, Loss: 0.0000009032849562\n",
      "Epoch: 280/2000, Loss: 0.0000009032849562\n",
      "Epoch: 290/2000, Loss: 0.0000009032849562\n",
      "Epoch: 300/2000, Loss: 0.0000009032849562\n",
      "Epoch: 310/2000, Loss: 0.0000009032849562\n",
      "Epoch: 320/2000, Loss: 0.0000009032849562\n",
      "Epoch: 330/2000, Loss: 0.0000009032849562\n",
      "Epoch: 340/2000, Loss: 0.0000009032849562\n",
      "Epoch: 350/2000, Loss: 0.0000009032849562\n",
      "Epoch: 360/2000, Loss: 0.0000009032849562\n",
      "Epoch: 370/2000, Loss: 0.0000009032849562\n",
      "Epoch: 380/2000, Loss: 0.0000009032849562\n",
      "Epoch: 390/2000, Loss: 0.0000009032849562\n",
      "Epoch: 400/2000, Loss: 0.0000009032849562\n",
      "Epoch: 410/2000, Loss: 0.0000009032849562\n",
      "Epoch: 420/2000, Loss: 0.0000009032849562\n",
      "Epoch: 430/2000, Loss: 0.0000009032849562\n",
      "Epoch: 440/2000, Loss: 0.0000009032849562\n",
      "Epoch: 450/2000, Loss: 0.0000009032849562\n",
      "Epoch: 460/2000, Loss: 0.0000009032849562\n",
      "Epoch: 470/2000, Loss: 0.0000009032849562\n",
      "Epoch: 480/2000, Loss: 0.0000009032849562\n",
      "Epoch: 490/2000, Loss: 0.0000009032849562\n",
      "Epoch: 500/2000, Loss: 0.0000009032849562\n",
      "Epoch: 510/2000, Loss: 0.0000009032849562\n",
      "Epoch: 520/2000, Loss: 0.0000009032849562\n",
      "Epoch: 530/2000, Loss: 0.0000009032849562\n",
      "Epoch: 540/2000, Loss: 0.0000009032849562\n",
      "Epoch: 550/2000, Loss: 0.0000009032849562\n",
      "Epoch: 560/2000, Loss: 0.0000009032849562\n",
      "Epoch: 570/2000, Loss: 0.0000009032849562\n",
      "Epoch: 580/2000, Loss: 0.0000009032849562\n",
      "Epoch: 590/2000, Loss: 0.0000009032849562\n",
      "Epoch: 600/2000, Loss: 0.0000009032849562\n",
      "Epoch: 610/2000, Loss: 0.0000009032849562\n",
      "Epoch: 620/2000, Loss: 0.0000009032849562\n",
      "Epoch: 630/2000, Loss: 0.0000009032849562\n",
      "Epoch: 640/2000, Loss: 0.0000009032849562\n",
      "Epoch: 650/2000, Loss: 0.0000009032849562\n",
      "Epoch: 660/2000, Loss: 0.0000009032849562\n",
      "Epoch: 670/2000, Loss: 0.0000009032849562\n",
      "Epoch: 680/2000, Loss: 0.0000009032849562\n",
      "Epoch: 690/2000, Loss: 0.0000009032849562\n",
      "Epoch: 700/2000, Loss: 0.0000009032849562\n",
      "Epoch: 710/2000, Loss: 0.0000009032849562\n",
      "Epoch: 720/2000, Loss: 0.0000009032849562\n",
      "Epoch: 730/2000, Loss: 0.0000009032849562\n",
      "Epoch: 740/2000, Loss: 0.0000009032849562\n",
      "Epoch: 750/2000, Loss: 0.0000009032849562\n",
      "Epoch: 760/2000, Loss: 0.0000009032849562\n",
      "Epoch: 770/2000, Loss: 0.0000009032849562\n",
      "Epoch: 780/2000, Loss: 0.0000009032849562\n",
      "Epoch: 790/2000, Loss: 0.0000009032849562\n",
      "Epoch: 800/2000, Loss: 0.0000009032849562\n",
      "Epoch: 810/2000, Loss: 0.0000009032849562\n",
      "Epoch: 820/2000, Loss: 0.0000009032849562\n",
      "Epoch: 830/2000, Loss: 0.0000009032849562\n",
      "Epoch: 840/2000, Loss: 0.0000009032849562\n",
      "Epoch: 850/2000, Loss: 0.0000009032849562\n",
      "Epoch: 860/2000, Loss: 0.0000009032849562\n",
      "Epoch: 870/2000, Loss: 0.0000009032849562\n",
      "Epoch: 880/2000, Loss: 0.0000009032849562\n",
      "Epoch: 890/2000, Loss: 0.0000009032849562\n",
      "Epoch: 900/2000, Loss: 0.0000009032849562\n",
      "Epoch: 910/2000, Loss: 0.0000009032849562\n",
      "Epoch: 920/2000, Loss: 0.0000009032849562\n",
      "Epoch: 930/2000, Loss: 0.0000009032849562\n",
      "Epoch: 940/2000, Loss: 0.0000009032849562\n",
      "Epoch: 950/2000, Loss: 0.0000009032849562\n",
      "Epoch: 960/2000, Loss: 0.0000009032849562\n",
      "Epoch: 970/2000, Loss: 0.0000009032849562\n",
      "Epoch: 980/2000, Loss: 0.0000009032849562\n",
      "Epoch: 990/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1000/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1010/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1020/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1030/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1040/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1050/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1060/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1070/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1080/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1090/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1100/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1110/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1120/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1130/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1140/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1150/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1160/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1170/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1180/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1190/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1200/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1210/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1220/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1230/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1240/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1250/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1260/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1270/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1280/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1290/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1300/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1310/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1320/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1330/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1340/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1350/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1360/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1370/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1380/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1390/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1400/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1410/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1420/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1430/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1440/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1450/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1460/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1470/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1480/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1490/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1500/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1510/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1520/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1530/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1540/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1550/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1560/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1570/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1580/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1590/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1600/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1610/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1620/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1630/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1640/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1650/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1660/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1670/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1680/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1690/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1700/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1710/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1720/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1730/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1740/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1750/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1760/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1770/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1780/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1790/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1800/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1810/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1820/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1830/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1840/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1850/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1860/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1870/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1880/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1890/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1900/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1910/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1920/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1930/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1940/2000, Loss: 0.0000009032849562\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1950/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1960/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1970/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1980/2000, Loss: 0.0000009032849562\n",
      "Epoch: 1990/2000, Loss: 0.0000009032849562\n",
      "Epoch: 2000/2000, Loss: 0.0000009032849562\n"
     ]
    }
   ],
   "source": [
    "# # dt=0.25, 0.15\n",
    "gru = GRU(input_size, hidden_size, output_size)\n",
    "\n",
    "# Loss and optimizer\n",
    "criterion = nn.MSELoss()\n",
    "optimizer = torch.optim.LBFGS(gru.parameters(), lr=0.1)\n",
    "\n",
    "\n",
    "# Training loop\n",
    "for epoch in range(num_epochs):\n",
    "    def closure():\n",
    "        optimizer.zero_grad()\n",
    "        hidden = torch.zeros(1, batch_size, hidden_size)\n",
    "\n",
    "        # Forward pass\n",
    "        output, hidden = gru(input_tensor, hidden)\n",
    "        loss = criterion(output, target_tensor)\n",
    "\n",
    "        loss.backward()\n",
    "        return loss\n",
    "\n",
    "    optimizer.step(closure)\n",
    "\n",
    "    # Print progress\n",
    "    if (epoch + 1) % 10 == 0:\n",
    "        print(f'Epoch: {epoch + 1}/{num_epochs}, Loss: {closure().item():.16f}')\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "144e7989",
   "metadata": {},
   "outputs": [],
   "source": [
    "# # Create GRU instance\n",
    "# gru = GRU(input_size, hidden_size, output_size)\n",
    "\n",
    "# # Loss and optimizer\n",
    "# criterion = nn.MSELoss()\n",
    "# optimizer = torch.optim.Adam(gru.parameters(), lr=0.01)\n",
    "\n",
    "# # Training loop\n",
    "# for epoch in range(num_epochs):\n",
    "#     # Set initial hidden state\n",
    "#     hidden = torch.zeros(1, batch_size, hidden_size)\n",
    "\n",
    "#     # Forward pass\n",
    "#     output, hidden = gru(input_tensor, hidden)\n",
    "#     loss = criterion(output, target_tensor)\n",
    "\n",
    "#     # Backward and optimize\n",
    "#     optimizer.zero_grad()\n",
    "#     loss.backward()\n",
    "#     optimizer.step()\n",
    "\n",
    "#     # Print progress\n",
    "#     if (epoch+1) % 10 == 0:\n",
    "#         print(f'Epoch: {epoch+1}/{num_epochs}, Loss: {loss.item():.8f}')\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "302b5fa0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1, 1, 201])\n",
      "torch.Size([1, 20, 201])\n"
     ]
    }
   ],
   "source": [
    "print(test_tensor.shape)\n",
    "prediction_tensor = torch.zeros(1, 20, 201).float()\n",
    "print(prediction_tensor.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "09f78c1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "with torch.no_grad():\n",
    "    hidden_pred = torch.zeros(1, batch_size, hidden_size)\n",
    "    prediction, _ = gru(test_tensor, hidden_pred)\n",
    "    prediction = prediction.view(1, 1, 201).float()\n",
    "    prediction_tensor[:, 0, :] = prediction\n",
    "    for i in range(19):\n",
    "        hidden_pred = torch.zeros(1, batch_size, hidden_size)\n",
    "        prediction, _ = gru(prediction, hidden_pred)\n",
    "        prediction = prediction.view(1, 1, 201).float()\n",
    "        prediction_tensor[:, i+1, :] = prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "879b8ce1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# exact\n",
    "u_test = u\n",
    "u_test_full = u_test[80:100, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "324eebba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([20, 201])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "k1 = (prediction_tensor - u_test_full)**2\n",
    "u_test_full_tensor = torch.tensor(u_test_full**2)\n",
    "u_test_full_tensor.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c4960438",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative Error Test:  0.4903226986347021 %\n"
     ]
    }
   ],
   "source": [
    "# Compute the relative L2 error norm (generalization error)\n",
    "relative_error_test = torch.mean(k1)/ torch.mean(u_test_full_tensor)\n",
    "\n",
    "print(\"Relative Error Test: \", relative_error_test.item(), \"%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "d95ba111",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.9381, dtype=torch.float64)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_abs = torch.max(prediction-u_test_full)\n",
    "R_abs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "198aa787",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.6303, dtype=torch.float64)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_mean = torch.mean(torch.abs(prediction - u_test_full))\n",
    "R_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "7d3966a6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Explained Variance Score: 0.40402867301019807\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "\n",
    "a = prediction\n",
    "b = u_test_full\n",
    "# Assuming 'a' is your predicted values (model's predictions) and 'b' is the true values (ground truth)\n",
    "# Make sure 'a' and 'b' are PyTorch tensors\n",
    "b = torch.tensor(b)\n",
    "# Calculate the mean of 'b'\n",
    "mean_b = torch.mean(b)\n",
    "\n",
    "# Calculate the Explained Variance Score\n",
    "numerator = torch.var(b - a)  # Variance of the differences between 'b' and 'a'\n",
    "denominator = torch.var(b)    # Variance of 'b'\n",
    "evs = 1 - numerator / denominator\n",
    "\n",
    "print(\"Explained Variance Score:\", evs.item())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "6251bfea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([20, 201])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction_tensor = torch.squeeze(prediction_tensor)\n",
    "prediction_tensor.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "5f5de2e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "conc_u = torch.squeeze(input_tensor)\n",
    "prediction_tensor = torch.squeeze(prediction_tensor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "5f3b7a32",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([100, 201])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "concatenated_tensor = torch.cat((conc_u, prediction_tensor), dim=0)\n",
    "\n",
    "concatenated_tensor.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "339e5891",
   "metadata": {},
   "outputs": [],
   "source": [
    "t1 = np.linspace(0, 1 , 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "159c6d5b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import torch\n",
    "\n",
    "# Create the figure and axis objects with reduced width\n",
    "fig, ax = plt.subplots(figsize=(5, 5))  # You can adjust the width (7 inches) and height (5 inches) as needed\n",
    "\n",
    "# # Make sure the font is Times Roman\n",
    "# plt.rcParams['font.family'] = 'Times New Roman'\n",
    "\n",
    "# # Perform the prediction\n",
    "# with torch.no_grad():\n",
    "#     prediction = lem(test_tensor)\n",
    "\n",
    "final_time_output = prediction_tensor[-2, :]\n",
    "final_out = final_time_output.detach().numpy().reshape(-1, 1)\n",
    "final_true = u[-2, :].reshape(-1, 1)\n",
    "\n",
    "# Plot the data with red and blue lines, one with dotted and one with solid style\n",
    "ax.plot(x.T, final_out, color='red', linestyle='dotted', linewidth=12, label='Prediction')\n",
    "ax.plot(x.T, final_true, color='blue', linestyle='solid', linewidth=7, label='True')\n",
    "\n",
    "# Set the axis labels with bold font weight\n",
    "ax.set_xlabel(r\"${x}$\", fontsize=26, color='black', fontdict={'weight': 'bold'})\n",
    "ax.set_ylabel(r\"${u(x, t)}$\", fontsize=26, color='black', fontdict={'weight': 'bold'})\n",
    "\n",
    "# Set the title with bold font weight\n",
    "ax.set_title(r\"${t = 0.99}$\", fontsize=26, color='black', fontweight='bold')\n",
    "\n",
    "# Set the number of ticks for x-axis and y-axis to 3\n",
    "ax.set_xticks([-1, 0, 1])\n",
    "ax.set_yticks([-1, 0, 1])\n",
    "\n",
    "# Set tick labels fontweight to bold and increase font size\n",
    "ax.tick_params(axis='both', which='major', labelsize=20, width=2, length=10)\n",
    "\n",
    "# # Set the fontweight for tick labels to bold\n",
    "# for tick in ax.get_xticklabels() + ax.get_yticklabels():\n",
    "#     tick.set_weight('bold')\n",
    "\n",
    "# Set the spines linewidth to bold\n",
    "ax.spines['top'].set_linewidth(2)\n",
    "ax.spines['right'].set_linewidth(2)\n",
    "ax.spines['bottom'].set_linewidth(2)\n",
    "ax.spines['left'].set_linewidth(2)\n",
    "\n",
    "\n",
    "# Increase font size for x and y axis numbers\n",
    "ax.tick_params(axis='both', which='major', labelsize=24)\n",
    "\n",
    "# Set the legend\n",
    "# ax.legend()\n",
    "\n",
    "plt.savefig('GRU_0.99_20.pdf', dpi=500, bbox_inches=\"tight\")\n",
    "\n",
    "# Show the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "6f25b2b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import torch\n",
    "\n",
    "# Create the figure and axis objects with reduced width\n",
    "fig, ax = plt.subplots(figsize=(5, 5))  # You can adjust the width (7 inches) and height (5 inches) as needed\n",
    "\n",
    "\n",
    "\n",
    "final_time_output = prediction_tensor[-20, :]\n",
    "final_out = final_time_output.detach().numpy().reshape(-1, 1)\n",
    "final_true = u[-20, :].reshape(-1, 1)\n",
    "\n",
    "# Plot the data with red and blue lines, one with dotted and one with solid style\n",
    "ax.plot(x.T, final_out, color='red', linestyle='dotted', linewidth=12, label='Prediction')\n",
    "ax.plot(x.T, final_true, color='blue', linestyle='solid', linewidth=7, label='True')\n",
    "\n",
    "# Set the axis labels with bold font weight\n",
    "ax.set_xlabel(r\"${x}$\", fontsize=26, color='black', fontdict={'weight': 'bold'})\n",
    "ax.set_ylabel(r\"${u(x, t)}$\", fontsize=26, color='black', fontdict={'weight': 'bold'})\n",
    "\n",
    "# Set the title with bold font weight\n",
    "ax.set_title(r\"${t = 0.81}$\", fontsize=26, color='black', fontweight='bold')\n",
    "\n",
    "# Set the number of ticks for x-axis and y-axis to 3\n",
    "ax.set_xticks([-1, 0, 1])\n",
    "ax.set_yticks([-1, 0, 1])\n",
    "\n",
    "# Set tick labels fontweight to bold and increase font size\n",
    "ax.tick_params(axis='both', which='major', labelsize=20, width=2, length=10)\n",
    "\n",
    "# # Set the fontweight for tick labels to bold\n",
    "# for tick in ax.get_xticklabels() + ax.get_yticklabels():\n",
    "#     tick.set_weight('bold')\n",
    "\n",
    "# Set the spines linewidth to bold\n",
    "ax.spines['top'].set_linewidth(2)\n",
    "ax.spines['right'].set_linewidth(2)\n",
    "ax.spines['bottom'].set_linewidth(2)\n",
    "ax.spines['left'].set_linewidth(2)\n",
    "\n",
    "# Set the legend\n",
    "# ax.legend()\n",
    "\n",
    "plt.savefig('GRU_0.81_20.pdf', dpi=500, bbox_inches=\"tight\")\n",
    "\n",
    "# Show the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "1de0e48b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import torch\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import FixedLocator\n",
    "\n",
    "# Assuming you have defined concatenated_tensor as a PyTorch tensor\n",
    "# concatenated_tensor = torch.cat((tensor1, tensor2), dim=0)\n",
    "\n",
    "# Convert concatenated_tensor to a NumPy array\n",
    "concatenated_array = concatenated_tensor.numpy()\n",
    "\n",
    "# Define custom color levels\n",
    "x = np.linspace(0, 1, concatenated_array.shape[1])  # Replace 0 and 1 with your actual x range\n",
    "t = np.linspace(0, 1, concatenated_array.shape[0])  # Replace 0 and 1 with your actual t range\n",
    "X, T = np.meshgrid(x, t1)\n",
    "\n",
    "# Define custom color levels using the minimum and maximum from the NumPy array\n",
    "c_levels = np.linspace(np.min(concatenated_array), np.max(concatenated_array), 400)\n",
    "\n",
    "# Plot the contour with interpolated data\n",
    "plt.figure(figsize=(20, 5))\n",
    "plt.pcolormesh(T, X, concatenated_array, shading='auto', cmap='coolwarm')\n",
    "\n",
    "# Set the fontweight for axis labels to regular (not bold)\n",
    "plt.xlabel(\"$t$\", fontsize=26)\n",
    "plt.ylabel(\"$x$\", fontsize=26)\n",
    "plt.title(\"$u(x, t)$\", fontsize=26)\n",
    "\n",
    "# Set tick labels fontweight to regular (not bold) and increase font size\n",
    "plt.tick_params(axis='both', which='major', labelsize=20, width=3, length=10)\n",
    "\n",
    "# Set the fontweight for tick labels to regular (not bold)\n",
    "for tick in plt.gca().get_xticklabels() + plt.gca().get_yticklabels():\n",
    "    tick.set_weight('normal')\n",
    "\n",
    "# Set the number of ticks for x-axis and y-axis to 5\n",
    "num_ticks = 5\n",
    "x_ticks = np.linspace(np.min(T), np.max(T), num_ticks)\n",
    "y_ticks = np.linspace(np.min(X), np.max(X), num_ticks)\n",
    "\n",
    "plt.gca().xaxis.set_major_locator(FixedLocator(x_ticks))\n",
    "plt.gca().yaxis.set_major_locator(FixedLocator(y_ticks))\n",
    "\n",
    "cbar1 = plt.colorbar()\n",
    "# Set the number of ticks for the color bar with uniformly distributed numbers\n",
    "num_ticks = 5\n",
    "c_ticks = np.linspace(np.min(concatenated_array), np.max(concatenated_array), num_ticks)\n",
    "cbar1.set_ticks(c_ticks)\n",
    "\n",
    "# Set the fontweight and fontsize for color bar tick labels\n",
    "for t in cbar1.ax.get_yticklabels():\n",
    "    t.set_weight('normal')\n",
    "    t.set_fontsize(26)  # Increase the font size for color bar tick labels\n",
    "\n",
    "# Increase the size of numbers on axis and color bar\n",
    "plt.xticks(fontsize=26)\n",
    "plt.yticks(fontsize=26)\n",
    "\n",
    "# Increase the tick size and width of the color bar\n",
    "cbar1.ax.tick_params(axis='both', which='major', labelsize=30, width=3,  length=10)\n",
    "\n",
    "# Add a dotted line at t = 0.8\n",
    "plt.axvline(x=0.8, color='black', linestyle='dotted', linewidth=5)\n",
    "\n",
    "#plt.savefig('Contour_LEM_20.pdf', dpi=500, bbox_inches=\"tight\")\n",
    "plt.savefig('contour_GRU_20.jpeg', dpi=500, bbox_inches=\"tight\")\n",
    "# Show the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4902f893",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "43c8e411",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e5425858",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "01ead432",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f6cc6a89",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8443d72e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f077c667",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "pytorch",
   "language": "python",
   "name": "pytorch"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
